Three-dimensional controlled-source electromagnetic induction algorithms ar
e generally formulated in terms of secondary fields or potentials. The sele
ction of the primary solution is somewhat arbitrary but can greatly influen
ce the efficiency of finite element codes. A simple induction logging probl
em demonstrates this statement. Responses are computed using a three-dimens
ional finite element method for two different selections of the primary pot
ential, one that includes the borehole effect and one that does not. The ac
curacy of the numerical solution, for a given mesh size, increases dramatic
ally when the borehole effect is included in the primary solution. This is
because the sharp gradients in the electromagnetic field near the transmitt
er due to the presence of the borehole are coded as an analytic source term
and do not have to be captured by the numerical approximation. Whenever po
ssible, finite element analysts should select a convenient primary solution
that closely matches the anticipated total solution in the immediate vicin
ity of the transmitter.